document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202324>Question 202324</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh>Elementary and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Open-top box. Thomas is going to make an open-top box<BR>\n" );
document.write( "by cutting equal squares from the four corners of an<BR>\n" );
document.write( "11 inch by 14 inch sheet of cardboard and folding up the<BR>\n" );
document.write( "sides. If the area of the base is to be 80 square inches, then<BR>\n" );
document.write( "what size square should be cut from each corner? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152555 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=152555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Thomas is going to make an open-top box<BR>\n" );
document.write( "by cutting equal squares from the four corners of an<BR>\n" );
document.write( "11 inch by 14 inch sheet of cardboard and folding up the<BR>\n" );
document.write( "sides. If the area of the base is to be 80 square inches, then<BR>\n" );
document.write( "what size square should be cut from each corner?<BR>\n" );
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document.write( "Draw a picture of the 80 sq. in sqare.<BR>\n" );
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document.write( "Cut an x by x square out of each corner of the cardboard<BR>\n" );
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document.write( "Since the cardboard was a square with area 80 sq. in, <BR>\n" );
document.write( "each side was sqrt(80) = 4sqrt(5)<BR>\n" );
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document.write( "Fold the sides up to form a height of \"x\" for the box.<BR>\n" );
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document.write( "The base of the box is a square with side = 4sqrt(5)-2x<BR>\n" );
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document.write( "The Volume of the box = x[4sqrt(5)-2x] = -2x^2 +4sqrt(5)x<BR>\n" );
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document.write( "This is a quadratic with a = -2, b = 4sqrt(5)<BR>\n" );
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document.write( "The maximum volume occurs when x = -b/2a = -4sqrt(5)/-4 = sqrt(5)<BR>\n" );
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document.write( "So the square you cut out of each corner should have a side of <BR>\n" );
document.write( "length sqrt(5).<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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